It looks like hives which come and go. Do not use any cosmetic products at the sites. You can apply some calamine lotion at the rash as it will help in soothing the skin. You can take some OTC oral antihistamine medications like Benadryl or Claritin and see if it helps.
For mild-moderate symptoms a weak steroid may be used (e.g. hydrocortisone as dermacort), whilst more severe cases require a higher-potency steroid (e.g. clobetasol propionate, fluocinonide).But they are available under prescription and should be taken only after consulting a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
Look up "eczema diet" or "what not to eat with eczema" or other related search terms. Not everyone with eczema needs to go gluten free, but, like you, I kept getting this rash (on my hands) that didn't seem to have any rhyme or reason. I for sure had eczema, but conventional doctors don't always recognize that diet definitely can play a huge role in the flare ups. That, in addition to what was mentioned, for sure. Sulfites are irritating to the skin, so definitely avoid sulfites from being in contact with the skin. There are definitely products that don't contain sulfites for personal care products, but you have to look for them, because if you don't know to look for these, you won't know that sulfites are in just about everything and you won't know that nowadays there are actually options out there. Look in the allergy community, because there is a post about sulfites that has a lot of information that will help you figure this out.
The best way to figure out if gluten is the culprit is to go on a trial elimination diet for gluten and/or dairy for at least a month to a month and a half before challenging the gluten by eating your usual gluten containing foods once again. If you break out after going back on gluten, then gluten is the culprit.